Definition 4.17 (TM-Induced Semimeasures tex2html_wrap_inline$_T,^M,^E,^G$)
Given some TM T,
for
define
.
Again we deviate a bit from Levin's B*-oriented path
[#!Zvonkin:70!#] (survey: [#!LiVitanyi:97!#, p. 245 ff, p. 272 ff])
and extend
to
,
where we define
.
If C denotes a set of TMs with universal element UC, then we write

(33)

We observe that
is universal among
all T-induced semimeasures, .
Note that

(34)

It will be obvious from the context when we deal with the
restriction of
to B*.

Corollary 4.2
For ,
is a CEM and approximable as the difference of two enumerable values:
for x without any 0-bit, otherwise